The effect of many-body interactions on the electrostatic force on a finite chain of spheres confined in a long charged tube

The effect of many-body interactions on the electrostatic force between spheres in a chain of charged spheres confined in a long charged pore has been quantified by solving the non-linear Poisson–Boltzmann equation (PBE), using the adaptive finite element method (AFEM) combined with error minimisation techniques. The equation is solved for conditions of constant surface potential and constant surface charge density. The computed force indicates that the force between any two spheres in a long chain of spheres in a long charged tube does not differ significantly from the force between only two spheres in a tube. This trend is also observed for an unconfined chain of spheres, where the force between two isolated spheres is again very similar to the force between any two spheres in a long unbounded chain. The results also quantify the effect of many-body interactions on the reduction of the repulsion force between the spheres. A significant reduction in the repulsion force between the spheres is observed when the radial distance between the pore wall and the chain of spheres is reduced. The effect of the dimensionless radius of the spheres on the electrostatic force between them has been determined and significant reduction of the force observed as the dimensionless radius is reduced.